Abstract
The finite difference discretization of the semiconductor equations yields symmetric, positive definite block-tridiagonal linear systems, which can be solved efficiently by the conjugate gradient method (CG). We have investigated several preconditioners with respect to vectorization to improve the simulation runtime. The performance of the different strategies has been evaluated on a CRAY C90 vector processor. We have found, that diagonal scaling can hardly be improved by additional incomplete Cholesky and polynomial preconditioners, because the reduction in the total number of iterations is usually compensated by the increased complexity of the preconditioned CG iteration. However, if the CG method is embedded in a nonlinear outer iteration, runtime savings have been obtained in some cases, because the preconditioned algorithms have produced a stable outer iteration with less stringent stopping criteria for the inner CG iterations.
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Thomas, S. (1997). Preconditioned conjugate gradient methods for semiconductor device simulation on a CRAY C90 vector processor. In: Palma, J.M.L.M., Dongarra, J. (eds) Vector and Parallel Processing — VECPAR'96. VECPAR 1996. Lecture Notes in Computer Science, vol 1215. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62828-2_118
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DOI: https://doi.org/10.1007/3-540-62828-2_118
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